How effective is a routine consisting entirely of push-ups and pull-ups for the upper body (excluding abs)? Does the volume matter for the answer to this question? Thank you.
Pushup and pullup workouts essentially cover all upper body muscle groups. When you are designing a workout plan the keys are looking for "pull" exercises and "push" exercises while incorporating core and legs.
Push exercises work typically on your chest and tricep muscles and pull exercises work on the back and bicep muscles. Pullups and pushups have lots of variations that can provide isolation to different muscle groups. Here are pushup variations and here are some pullup variations.
The advantages of weight training over are isolation and it can be a little faster but you can get similar results for bodyweight exercises.
Either way whether weekend warrior or pro athlete bodyweight alone is still effective. There are plenty of testimonials you can look online to show that bodyweight exercise is effective.
Just gonna throw out some personal experience here: I have had good luck with Nike Training Club and Freeletics. They both have bodyweight variations that are quite effective and cover all muscle groups.